Inverse hyperbolic problems with time-dependent coefficients

Details Inverse hyperbolic problems with time-dependent coefficients Inverse hyperbolic problems with time-dependent coefficients

2005-08-09

arxiv.org/abs/math/0508161v2

Mathematics

Analysis of PDEs

The main change is the use of BLR-condition to fill the gap in the proof of the main theorem

Scientific paper

We consider the inverse problem for the second order self-adjoint hyperbolic equation in a bounded domain in $\R^n$ with lower order terms depending analytically on the time variable. We prove that, assuming the BLR condition, the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the hyperbolic equation up to a diffeomorphism and a gauge transformation. As a by-product we prove a similar result for the nonself-adjoint hyperbolic operator with time-independent coefficients.

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